Question

In the chess club with 12 members, the average age was 63 years. Göran, 70 years old old, quits the club. Then a new member of the club starts. Otto, 13 years old old. How to change a) Average age? b) Median age?

Answer 1

The average age in the chess club will decrease from 63 to approximately 58.25 years after Göran leaves and Otto joins. The median age will likely decrease as well, especially if the original ages were not symmetrically distributed, but we need all the individual ages to compute the exact new median.

Step-by-step explanation:

To determine the changes in the average age and median age when Göran quits the chess club and Otto joins, we can follow these steps:

Calculate the total age of all members before any changes.

Adjust the total age to account for the members leaving and joining.

Recalculate the average age with the new total age and the number of members.

Analyze the change in median age based on the ages of the members.

Before Göran quits, the total age of 12 members with an average age of 63 years is 12 * 63 = 756 years.

After Göran quits and before Otto joins, the total age is 756 - 70 = 686 years.

Once Otto joins, the total age becomes 686 + 13 = 699 years with 12 members. The new average age is 699 / 12 ≈ 58.25 years.

Regarding the median age:

If Göran's age of 70 years was not one of the median values, the addition of Otto, being much younger, could lower the median value, if the ages are not equally distributed above and below the median.

We would need all the individual ages to calculate the exact median age after the changes.

Thus, without all individual ages, we can only conclude that the average age will decrease from 63 to approximately 58.25 years, and the median age will likely decrease, particularly if the ages are not symmetrically distributed before the change.